Proceeding of IC-ITS 2015 e-ISBN:978-967-0850-07-8
International Conference on Information Technology & Society
8-9 June 2015, Kuala Lumpur, MALAYSIA
An Optimized Neuro-Fuzzy Network based Image
Denoising Techniques
Dr.M.Soranamageswaria and M.Sindhana Devib
a. Assistant Professor, Post Graduate and Research Department of Computer science,
Government Arts College(Autonomous), Coimbatore, Tamil Nadu, India.
b. Research Scholar, Post Graduate and Research Department of Computer science,
Government Arts College(Autonomous), Coimbatore, Tamil Nadu, India.
[email protected]
Abstract. Neuro-Fuzzy (NF) system is used in various field of research. Neuro-Fuzzy
systems combining neural networks and fuzzy set theories can be employed as
powerful tools for the removal of impulse noise from various images. Neuro-Fuzzy
system is based on a fuzzy system which is trained by learning algorithm derived from
neural network theory. The learning procedure operates on local information, and
causes local modifications in underlying fuzzy system. Image noise is random (not
present in the object image) variation or brightness or color information in images, and
is generally an aspect of electronic noise. It can be produced by sensor and circuitry of
scanner or a digital camera. Images are often corrupted by noise during the acquisition
or transmission process. The goal of denoising is to remove the noise while retaining
as much as possible the important signal features of an image.
Neuro-Fuzzy network based impulse noise filtering for gray scale images is presented.
The proposed method is constructed by hybrid technique of Mamdani and Sugeno
based fuzzy interference system approach followed by Optimized intelligent water
drop(IWD) technique, Tuning parameter approach, Optimized fuzzy intelligence noise
filter approach. As demonstrated by experimental results, Peak signal-to-noise
ratio(PSNR) and Root Mean Square Error(RMSE) possess better performance. The
proposed
filter
has
some
advantages
over
its
competitors.
The hybrid rule is applied to reduce the error of the optimization. In hybrid based
fuzzy interference system approach, the system develops a fuzzy logic based scheme
to filter a noisy signal. This can be applied in various sources to reduce noise. A one
input and output Mamdani fuzzy interference system is designed for the filter where
the input is a noisy signal and output is a filtered output. Fuzzy rules have been used to
obtain the filtered output.
Keywords: Neuro-Fuzzy, image processing, hybrid technique.
INTRODUCTION
Noise is any undesired information that contaminates an image. Noise appears in an
image from a variety of sources. Removal of noises from the images is a critical issue in
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Proceeding of IC-ITS 2015 e-ISBN:978-967-0850-07-8
International Conference on Information Technology & Society
8-9 June 2015, Kuala Lumpur, MALAYSIA
the field of digital image processing. Image denoising is an important image processing
task both as a process itself, and as a component in some other processes. The main
property of a good image denoising model is that it will remove noise while preserving
edges. Usually, linear models have been used. But the back draw of a linear model is that
they are not able to preserve edges in a good way. Edges, which are recognized as
discontinuities in the image, are smeared out. Thus noise cancellation or noise filtering is
an important task in image processing, mainly when the final product is used for edge
detection, image segmentation, and data compression.
The neuro fuzzy network based image denoising for gray scale images is presented in
this paper. In this case, non linear techniques perform better than linear filters. This leads
to blur the edges. The impulse noise filter consists of two modes of operation, namely,
training and testing (filtering). During training process, each Neuro-Fuzzy (NF) filter is
trained individually by using a simple artificial training image and the internal parameters
of each NF filter are adaptively optimized. During testing process, the outputs of two NF
filters are fed to the postprocessor, which in turn generates the final output of the
proposed filter. The main filtering methods to remove the noise from images are based
median filtering techniques
The paper is organized as follows. In section 2, the proposed method of neuro fuzzy
filter and the hybrid technique is discussed. The experimental analyses are described in
section 3 and the final section summarizes the paper.
THE PROPOSED METHOD
The proposed system deals with operating the pixel values. Two district pixels are
obtained in the 3-by-3 pixel filtering window. Hence, the first pixel takes the horizontal
direction and the corresponding second pixel obtains the vertical direction. In figure.1 the
middle pixel P2 is the existing one under in operation, the rest pixels P1 and P3 are
mentioned for operations centering the middle P2 pixel.
(a)
(b)
P1
P2
P1
P2
P3
P3
FIGURE 1. Two neighbourhood pixels. (a)Vertical direction, (b)Horozontal direction.
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Proceeding of IC-ITS 2015 e-ISBN:978-967-0850-07-8
International Conference on Information Technology & Society
8-9 June 2015, Kuala Lumpur, MALAYSIA
Fuzzy rules have been used to obtain the filtered output. The de-fuzzier filter output
has been obtained using centroid method. In Mamdani based fuzzy interference system
(FIS) Approach m11,m12,m13… are the membership function. The membership values take
place between 0 to 1. The membership function gives the best solution for remove the
noisy from various images.
The four inputs of each NF filter, x1, x2, x3, and x4, can be defined as follows:
X1=p1-m
X2=p2-m
X3=p3-m
X4=m.
Neuro Fuzzy System
A neuro-fuzzy system is a fuzzy system that uses a learning algorithm derived from or
inspired by neural network theory to determine its parameters (fuzzy sets and fuzzy rules)
by processing data samples. Modern neuro-Fuzzy systems are usually represented as
special multilayer feedforward neural networks. However, fuzzificatios are also
considered, for example self-organizing feature maps. A neuro-fuzzy system is based on
a fuzzy system which is trained by learning algorithm derived from neural network
theory. The learning procedure operates on local information, and causes only local
modification in the underlying fuzzy system.
A neuro-fuzzy system can be viewed as a 3-layer feedforward neural network. The
first layer represents input variables, the middle (hidden) layer represents fuzzy rules and
the third layer represents output variables. Fuzzy sets are encoded as connection weights.
Sometimes 5-layer architecture is used, where the fuzzy sets are represented in the units
of the second and fourth layer.
The internal structures of the two NF filters are identical to each other. Each of them is
a first order Sugeno type fuzzy inference system with 4-inputs and 1-output. Each input
has three generalized bell type membership functions and the output has a linear
membership function. While the NF filter has 4 inputs and each input has 3 membership
functions, the rule base contains a total of 81(34) rules defined as follows:
Rule1: if (x1 is M11) and (x2 is M21) and (x3 is M31) and
(x4 is M41) then y1 = d11x1+ d12x2+ d13x3+ d14x4+ d15
Rule2: if(x1 is M11) and (x2 is M21) and (x3 is M31) and
(x4 is M42) then y2 = d21x1+ d22x2+d23x3+d24x4+d25
Rule3:if (x1 is M11) and (x2 is M21) and (x3 is M31) and
(x4 is M43) theny3 =d31x1+d32x2+d33x3+d34x4+d35
.
.
.
Rule 81:if (x1 is M13) and (x2 is M23) and (x3 is M33) and
(x4 is M43) then y81 = d81,1x1+d81,2x2+d81,3x3+d81,4x4+d81,5
where Mij denotes the jth membership function of the ith input, yk denotes the output of
the kth rule, dkl is the consequent parameter, i = 1; 2; 3; 4, j =1; 2; 3, k = 1,…, 81, l= 1, 2,
3, 4, 5.
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Proceeding of IC-ITS 2015 e-ISBN:978-967-0850-07-8
International Conference on Information Technology & Society
8-9 June 2015, Kuala Lumpur, MALAYSIA
The hybrid technique
To deal with the problem of the image, the current work contributes the following
methods for noise reduction. The proposed method is constructed by the following
approaches,
1. Hybrid technique of Mamdani and Sugeno based fuzzy interference system
approach,
2. Optimized intelligent water drop(IWD) technique,
3. Tuning parameter approach,
4. Optimized fuzzy intelligence noise filter approach.
This system is constructed by combining two NF filters with a postprocessor. Each of the
two NF filters is a first order Sugeno and Mamdani type fuzzy inference system with 4inputs and 1-output. As for each pixel of the input image, the four inputs of each NF
filter, x1, x2, x3, and x4, are obtained by selecting the data block, respectively. The
system develops a fuzzy logic based scheme to filter a noisy signal. This can be applied
in various sources to reduce noise. A one input and one output Mamdani fuzzy
interference system is designed for the filter where the input is noisy signal and the
output is a filtered output.
Filtered
Output
Noisy Signal
Data block
Selection
Neuro
Fuzzy Filter
Hybrid
Technique
FIGURE 2. The structure of hybrid technique method
Noise is a factor that degrades the quality of images, so we need to use an efficient
technique to remove the noise from the image. Fig.2 shows the structure of hybrid
technique, where the noisy signal is the input and the output is a filtered output.
EXPERIMENTAL RESULTS
Experimental results are presented in this section to demonstrate the performance of
the proposed hybrid technique of Mamdani and Sugeno based fuzzy interference system
approach. In our simulation, six original images shown in Fig. 3 are 8-bit gray scale
images with the same size of 256-by-256 pixels. The system method has used the design
of experiments in order to find an optimum combination of parameters, which could have
an effect on the performance of the system.
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Proceeding of IC-ITS 2015 e-ISBN:978-967-0850-07-8
International Conference on Information Technology & Society
8-9 June 2015, Kuala Lumpur, MALAYSIA
(a)
(d)
(b)
(e)
(c)
(f)
FIGURE 3. Testing Images: (a) Airplane; (b) Barbara; (c) Baboon; (d) Boat; (e) Lena; (f) Peppers
The system considered peak signal-to-noise-ratio (PSNR) for finding the optimum
combination of parameter and Root mean square error (RMSE). The peak signal-to-noise
ratio, abbreviated PSNR, is an engineering term for the ratio between the maximum
possible power of a signal and the power of corrupting noise that affects the fidelity of its
representation. Since many signals have a very wide dynamic range, PSNR is generally
expressed in terms of the logarithmic decibel scale. The mean squared error (MSE) of an
estimator is one of many ways to quantify the difference between values implied by an
estimator and the true values of the quantity being anticipated. MSE is a risk function,
corresponding to the expected value of the squared error loss or quadratic loss. MSE
measure the average of the squares of the "errors." The error is the amount by which the
value implied by the estimator differs from the quantity to be anticipated. The difference
occurs because of randomness or because the estimator doesn't account for information
that could produce a more accurate estimate.
TABLE (1). Comparison of PSNR values for different images.
Name of the image
NF(Sugeno)
NF(Hybrid technique)
Airplane
33.2734
42.7512
Barbara
39.5834
43.9042
Baboon
37.5293
45.6440
Boat
37.9497
44.0316
Leena
39.0300
44.6049
Peppers
42.2369
42.7693
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Proceeding of IC-ITS 2015 e-ISBN:978-967-0850-07-8
International Conference on Information Technology & Society
8-9 June 2015, Kuala Lumpur, MALAYSIA
TABLE (2). Comparison of RMSE values for different images.
Name of the image
NF(Sugeno)
NF(Hybrid technique)
Airplane
1.3699
0.5034
Barbara
0.6876
0.4179
Baboon
0.8710
0.3422
Boat
0.8298
0.4120
Leena
0.7328
0.3857
Peppers
0.5066
0.4764
`
The above table shows, the proposed hybrid method of Mamdani and Sugeno
performed well than the existing one. The proposed method of PSNR results in higher
value and the MSE gives the least effective among the methods compared. It is easy to
implement over smooth the images.
PSNR values
CHART(1). COMPARISON OF PSNR VALUES FOR DIFFERENT IMAGES.
50
40
30
20
10
0
NF(Sugeno)
NF(Hybrid
technique)
Images
RMSE values
CHART(2). COMPARISON OF RMSE VALUES FOR DIFFERENT IMAGES
1.5
1
NF(Sugeno)
0.5
0
NF(Hybrid
technique)
Images
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Proceeding of IC-ITS 2015 e-ISBN:978-967-0850-07-8
International Conference on Information Technology & Society
8-9 June 2015, Kuala Lumpur, MALAYSIA
CONCLUSION
An optimized neuro-fuzzy network based image denoising technique for gray scale
images was presented in this paper. The proposed method is constructed by hybrid
technique of Mamdani and Sugeno based fuzzy interference system approach followed
by Optimized intelligent water drop (IWD) technique, Tuning parameter approach,
Optimized fuzzy intelligence noise filter approach. As supported by the simulation
results, the proposed technique compares favorably with conventional techniques in the
capabilities of noise reduction and detail preservation.
REFERENCES
1. Anil K.Jain, (1989). Fundamentals of Digital Image Processing, first edition, Prentice
– Hall, Inc.
2. J.J. Buckley and Y.Hayashi,(1995). Neural networks for Fuzzy systems: Fuzzy sets
ans systems 71, 265-276.
3. M.T. Hagan, H.B. Demuth, M. Beale,(1996) Neural Network Design, PWS
Publishing, Boston, MA,
4. M.E. Yuksel, A hybrid neuro-fuzzy filter for edge preserving restoration of images
corrupted by impulse noise, IEEETrans.ImageProcess.15(4)(2006) 928–936.
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